1)sin2xsin3x+cos5x=0
1/2(cos(2x-3x)-cos(2x+3x))+cos5x=0
1/2cosx-1/2cos5x+cos5x=0
1/2cosx+1/2cos5x=0
cosx+cos5x=0
2cos3xcos2x=0
cos3x=0 cos2x=0
3x=π/2+πn 2x=π/2+πk
x=π/6+πn/3 n∈Z x=π/4+πk/2 k∈Z
2)cosx-cos3xcos2x=0
cosx-1/2(cos(3x-2x)+cos(3x+2x))=0
cosx-1/2cosx-1/2cos5x=0
1/2cosx-1/2cos5x=0
cosx-cos5x=0
2sin3xsin2x=0
sin3x=0 sin2x=0
3x=πn 2x=πk
x=πn/3 n∈Z x=πk/2 k∈Z
3)sin2xcos5x+sin3x=0
1/2(sin(-3x)+sin7x)+sin3x=0
-1/2sin3x+1/2sin7x+sin3x=0
1/2sin3x+1/2sin7x=0
sin3x+sin7x=0
2sin5xcos(-2x)=0
2sin5xcos2x=0
sin5x=0 cos2x=0
5x=πn 2x=π/2+πk
x=πn/5 n∈Z x=π/4+πk/2 k∈Z
4)sin7x-cos3xsin4x=0
sin7x-1/2(sin(-x)+sin7x)=0
sin7x+1/2sinx-1/2sin7x=0
1/2sin7x+1/2sinx=0
sin7x+sinx=0
2sin4xcos3x=0
sin4x=0 cos3x=0
4x=πn 3x=π/2+πk
x=πn/4 n∈Z x=π/6+πk/3 k∈Z
Решение смотри во вложении.
28x^2 + 5x + 8
D = 25 - 896 = - 871
D < 0
ОТВЕТ нет корней
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4x^2 - 6x + 2 = 0
D = 36 - 32 = 4 = 2^2
x1 = ( 6 + 2 ) : 8 = 1
x2 = ( 6 - 2 ) : 8 = 0,5
1 > 0,5
Ответ 1 ; 0,5